1MS.3 MATEMÀTICA FINANCERA/1MS.3.4 Anualitat de capitalització 1MS.3.4.10DT CAPITALITZACIÓ

Anualitat de capitalització

Si ingressem un capital A durant t anys a un interès anual r, es genera un capital C:
C = A(1+r) + A(1+r)² + ... + A(1+r)^t
= A(1+r) [1 + (1+r) + ... (1+r)^t-1]
i aplicant la fórmula de la suma dels termes d'una progressió geomètrica:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»C«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»r«/mi»«msup»«mo mathvariant=¨bold¨»)«/mo»«mi mathvariant=¨bold¨»t«/mi»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mi mathvariant=¨bold¨»r«/mi»«/mfrac»«/math»

Si el plaç és inferior a l'any, cal transformar r en r/f i t en f·t on f és la freqüència de pagament d'interessos

]]> 0.0000000 0.0000000 0 1MS.3.4.11Q CàlculC(anys) Si ingressem, cada any, durant #t anys #A € a un interès del #i %, quin capital tindrem al final del procés?

Resposta arrodonida al cèntims.

]]> 1.0000000 0.5000000 0 0 #C <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mi>i</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi><mo>=</mo><mi>A</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><mo>)</mo><mo>*</mo><mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><msup><mo>)</mo><mi>t</mi></msup><mo>-</mo><mn>1</mn></mrow><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>C_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5600</mn><mo>,</mo><mn>4.3</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.043</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>46555.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#C</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal aplicar la fórmula.

]]> 1MS.3.4.15Q CàlculA(anys) Quina quantitat hem ingressat cada any, durant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»t«/mi»«/mrow»«/mstyle»«/math» anys, a un interès compost anual del «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«/mrow»«/mstyle»«/math» %, si hem recollit en total «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»C«/mi»«/mrow»«/mstyle»«/math» €?

Resposta arrodonida a la centena.

]]> 1.0000000 0.5000000 0 0 #A <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mi>i</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi><mo>=</mo><mi>A</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><mo>)</mo><mo>*</mo><mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><msup><mo>)</mo><mi>t</mi></msup><mo>-</mo><mn>1</mn></mrow><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>C_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfrac><mrow><mi>s</mi><mo>*</mo><mi>C_1</mi></mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><mo>)</mo><mo>*</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>s</mi></mrow></mfenced><mi>t</mi></msup><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#A</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal aïllar A en la fórmula:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»C«/mi»«mo mathvariant=¨bold¨»*«/mo»«mi mathvariant=¨bold¨»r«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold-italic¨»r«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced open=¨[¨ close=¨]¨»«mrow»«msup»«mfenced»«mrow»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold-italic¨»r«/mi»«/mrow»«/mfenced»«mi mathvariant=¨bold¨»t«/mi»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mstyle»«/math»
]]> 1MS.3.4.21Q CàlculA(mensualitat) Durant els #t anys de la seva vida laboral, en Lluc ha ingressat cada mes una certa quantitat en una entitat bancària per constituir un pla de pensions, amb un interès anual compost del #i %.

Quan es jubila, li donen el capital final del qual es gasta #g11 € fins que es mor i deixa la resta, #h euros, en herència.

Quina quantitat havia ingressat cada mes?

a) Calcula primer quant li ha donat el banc a partir del que gasta i del que deixa en herència.

b) Aplica la fórmula per calcular la mensualitat (tenint present que f =12)

Resposta arrodonida als cèntims.

]]> 1.0000000 0.5000000 0 0 a) =#Cb) =#A]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mi>i</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>2000</mn><mo>·</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>1000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g11</mi><mo>=</mo><mi>q</mi><mo>*</mo><mn>12</mn><mo>+</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>g11</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>=</mo><mfrac><mrow><mi>C</mi><mo>*</mo><mfrac><mi>s</mi><mn>12</mn></mfrac></mrow><mrow><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mi>s</mi><mn>12</mn></mfrac></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mi>s</mi><mn>12</mn></mfrac></mrow></mfenced><mrow><mn>12</mn><mo>*</mo><mi>t</mi></mrow></msup><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mi>A1</mi></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>,</mo><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>,</mo><mn>4.6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g11</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>C</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>168020</mn><mo>,</mo><mn>6000</mn><mo>,</mo><mn>174020</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>224.17</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>C</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>A</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El que li dona el banc és C = #g11 + #h

Només cal aïllar A en la fórmula:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»C«/mi»«mo mathvariant=¨bold¨»*«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»i«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced open=¨[¨ close=¨]¨»«mrow»«msup»«mfenced»«mrow»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mfenced»«mi mathvariant=¨bold¨»t«/mi»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1MS.3.4.25Q CàlculTemps(anualitats) Durant quants anys hem ingressat cada any #A €, a un interès del #i %, si hem recollit #C €?

Resposta arrodonida a la unitat.

]]> 1.0000000 0.5000000 0 0 #t <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mi>i</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi><mo>=</mo><mi>A</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><mo>)</mo><mo>*</mo><mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><msup><mo>)</mo><mi>t</mi></msup><mo>-</mo><mn>1</mn></mrow><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>C_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfrac><mrow><mi>s</mi><mo>*</mo><mi>C_1</mi></mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><mo>)</mo><mo>*</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>s</mi></mrow></mfenced><mi>t</mi></msup><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#t</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal aïllar t en la fórmula.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»log«/mi»«mstyle displaystyle=¨true¨»«mfrac»«mrow»«mi mathvariant=¨bold¨»C«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»r«/mi»«/mrow»«mrow»«mi mathvariant=¨bold¨»A«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»r«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mstyle»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mi mathvariant=¨bold¨»log«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»r«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=e30bc827c55b2f1286f4ae618ac5f1fa&cw=124&ch=44&cb=32" width="124" height="44" style="vertical-align: -12px;"/>

]]> 1MS.3.4.51 PlaPensionsAnual Una persona aporta cada any a un un pla de pensions #A €. Quan es jubili, d'aquí a #t anys quina quantitat rebrà si l'interès del pla és del #i %?

Resposta arrodonida al cèntims.

]]> 1.0000000 0.5000000 0 0 #C <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>35</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mi>i</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi><mo>=</mo><mi>A</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><mo>)</mo><mo>*</mo><mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><msup><mo>)</mo><mi>t</mi></msup><mo>-</mo><mn>1</mn></mrow><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>C_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#C</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aplica la fórmula per calcular C

]]> 1MS.3.4.61Q PlaPensionsMensual Una persona aporta cada mes a un un pla de pensions #A €. Quan es jubili, d'aquí a #t anys quina quantitat rebrà si l'interès del pla és del #i % i el període de capitalització ha estat d'un mes?

Resposta arrodonida al cèntims.

]]> 1.0000000 0.5000000 0 0 #C <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>35</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mi>i</mi><mn>1200</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi><mo>=</mo><mi>A</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><mo>)</mo><mo>*</mo><mfrac><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>s</mi><msup><mo>)</mo><mrow><mn>12</mn><mo>*</mo><mi>t</mi></mrow></msup><mo>-</mo><mn>1</mn></mrow><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>C_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8.04</mn><mo>*</mo><msup><mn>10</mn><mn>5</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#C</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> S'aplica la fórmula de la capitalització per calcular C, tenint present que la freqüència es mensual i, per tant, f = 12; cal doncs dividir la taxa d'interès per 12 i multiplicar el temps per 12.

]]>